The answer you got on sports is pretty complete, although a bit off in the muscle explanation.
You want a good solid core and complementary arm strength, coupled with a solid foundation. I would suggest full body exercises such as pushups, squats, plank work, and to specifically work some of the rotational muscles I would add cable chops from high to low and low to high.
Flexibility is also going to be a big factor in your swing. If you aren't flexible, then the only way to get more shoulder turn (And thus a longer arc which in turn gives you more time to accelerate the club) is to start lifting your arms away from your body, which will give you that flying elbow problem.
The other advice about matching your equipment is excellent, I was using a regular flex shaft, and couldn't control it because I was overpowering it and it was way too whippy. If you start accelerating more, then you may have to look at getting a stiffer flex. Conversely, if your shaft is too rigid for your swing, then you are actually losing distance because you aren't getting as much out of your club, because you aren't moving fast enough to get the shaft to flex and then come through the ball.
It is a typical golfer response to look at your equipment, but that's actually the first place I'd look, especially considering you already have a straight ball flight. Find somewhere that can measure your swing speed over several different clubs, and match your shafts to your swing speed.
Do that and add more flexibility and resisted rotation work, and I would guesstimate you could get into the 250 range pretty easily, and probably still maintain the accuracy.